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Strength of Shafts.


Example 16.A foundation bolt with square head (Fig. 368) is
secured by a cotter. Find D, b, and / in terms of d> where ft,fs, andyi
vary as I : | : 2 respectively. (Hons. Mach. Constr. Exam. 1886.)

Following the previous calculations :

D = ro8 d,   b = 1-44 d^    and t"*f>z d.


Torsional Stress-Action unallied with bending occurs
only in very short shafts. In any case the two actions Ihust be
separately considered. Fig. 369 shews a shaft under twist, the
external load being caused by the couple dxb c, while the in-
ternal resistance of the shaft is shewn by the couple exfg*

.-.    External mometitjlmoment of resistance of section
or    W>=/sZt

where Zt, the modulus of section, is a number depending on the
size and shape of the section.

Strength of Solid Round Shaft.Let r be the outer
radius of a solid shaft, Fig. 370. Imagining the section divided
into concentric rings:

Total stress on outer ring =/s X2irrxt               (i)

Bntfs diminishes towards the centre because l>5 decreases:
.-.   Total stress at any other ring ^ = -fs x 21?^ x t     (2)

* A couple is formed by a pair of equal and opposite forces, and can pro-
duce turning effect only, being represented by 'one force x "total arm.'